It may be that the fear is not so much related to the responsibility to the child itself, but to some other aspects. For example, many men may be anxious about their role in this child's life: will they be comfortable being a part of the child's life and influencing his upbringing? There may be concerns about the mother's past relationships and how that might affect the new relationship.
In addition, an emotional investment in a relationship with a woman with a child may mean not only an investment in the relationship itself, but also in the child. This entails a deep emotional responsibility and a level of involvement that can cause apprehension and anxiety.
Yes, any relationship carries with it certain types of responsibility. However, in the case of a relationship with a woman who has a child, that responsibility can seem more complex and profound because of the additional dynamics involved.
I think it's important to realize that all of these concerns are quite normal and part of the decision-making process of entering into such a relationship. A relationship with a woman who has a child requires more deliberation and willingness to accept this additional responsibility. But ultimately, if mutual love, respect and a willingness to understand are present, such a relationship can be as happy and satisfying as any other.
I sincerely hope that these reflections will help you realize that fears and concerns about such relationships are part of the process of realizing them, but should not be an obstacle to possible happiness and harmony.